Sinkhorn Permutation Variational Marginal Inference
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Proceedings of The 2nd Symposium on
Advances in Approximate Bayesian Inference, PMLR 118:19, 2020.
Abstract
We address the problem of marginal inference for an exponential family defined over the set of permutation matrices. This problem is known to quickly become intractable as the size of the permutation increases, since its involves the computation of the permanent of a matrix, a #Phard problem. We introduce Sinkhorn variational marginal inference as a scalable alternative, a method whose validity is ultimately justified by the socalled Sinkhorn approximation of the permanent. We demonstrate the effectiveness of our method in the problem of probabilistic identification of neurons in the worm C.elegans.
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